On inclusions between Arbault sets
Peter Eliaš · Czech digital mathematics library · 2003
We show that two Arbault sets characterized by increasing sequences of natural numbers are in inclusion if and only if one of these sequences is derived from another in a special way.A set X ^ R is called an Arbault set if there exists an increasing sequence a e N N such that for all xeX, lim sin na(n) x = 0. J. Arbault considered this kind of sets when he studied the sets of absolute convergence of trigonometric series [1].We denote by si the family of all Arbault sets.Here are some properties of the family si (for more, see e.g.[2]).